Generalized nonextensive power-law transverse momentum spectra and their applications in high-energy collision physics

High energy collision events (proton-proton, lead-lead etc.) create the quark-gluon plasma (QGP), a state of matter in which the micro-second old universe existed. Distribution of particles created in these events help understand the properties of QGP.

Experiments (e.g., the LHC at CERN) have given rise to many theoretical and phenomenological studies attempting to describe particle (hadron) production, which follows a power-law distribution, using statistical models.

Hadron spectra generated in high-energy collisions are described by nonextensive distributions in the transverse momentum space represented by two parameters, the nonextensivity parameter q and temperature T. The nonextensive distributions approach the Boltzmann-Gibbs distributions in the limit q approaching 1.

The nonextensive distributions, widely used in the phenomenological studies, can be calculated from statistical mechanics using constrained maximization of a generalized nonextensive entropy. The project GLITTER concentrates on these distributions and is divided into two parts: theory and phenomenology.

In the theory part, the analytical form of the most generalized nonextensive transverse momentum spectra without an existing procedural arbitrariness will be calculated using nonextensive statistical mechanics for a simple harmonic oscillator.

Also, a nonextensive model for an anisotropic medium will be proposed for arbitrary energy using the Mellin-Barnes representation.

In the second part, phenomenological implications of these models will be explored using the ROOT programs that will be set up using the expertise of the supervisor's group.

The project will propose analytical nonextensive models generalizing existing results and leading to reduced computation time.

It will also clear the ambiguity regarding the usage of various forms of nonextensive distributions, will offer a firm basis for the studies in the field, and will generate many updated information about the properties of QGP.